Related papers: An efficient approach to global sensitivity analys…
Measuring scattered light is central to many laser-based gas diagnostic techniques, e.g., coherent anti-Stokes Raman spectroscopy (CARS) and filtered Rayleigh scattering (FRS). To produce quantitative measurements with such techniques, a…
Scattering-type scanning near-field optical microscopy is becoming a premier method for the nanoscale optical investigation of materials well beyond the diffraction limit. A number of popular numerical methods exist to predict the…
Multiple scattering of an electromagnetic wave as it passes through an object is a fundamental problem that limits the performance of current imaging systems. In this paper, we describe a new technique-called Series Expansion with…
Global quantum sensing enables parameter estimation across arbitrary ranges with a finite number of measurements. Among the various existing formulations, the Bayesian paradigm stands as a flexible approach for optimal protocol design under…
We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy…
A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and non-linear, therefore computationally expensive. An emulator-based methodology is…
Lamellar gratings are widely used diffractive optical elements; gratings etched into Si can be used as structural elements or prototypes of structural elements in integrated electronic circuits. For the control of the lithographic…
Uncertainty in physical parameters can make the solution of forward or inverse light scattering problems in astrophysical, biological, and atmospheric sensing applications, cost prohibitive for real-time applications. For example, given a…
This paper presents an efficient surrogate modeling strategy for the uncertainty quantification and Bayesian calibration of a hydrological model. In particular, a process-based dynamical urban drainage simulator that predicts the discharge…
We show how to apply Sobol's method of global sensitivity analysis to measure the influence exerted by a set of nodes' evidence on a quantity of interest expressed by a Bayesian network. Our method exploits the network structure so as to…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of a passive scalar (e.g., the concentration of a pollutant).…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…
We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the graph to a matrix initial-boundary value (IBV) problem and then…
In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian framework. Here, the focus is on…
A method is developed for fitting theoretically predicted astronomical spectra to an observed spectrum. Using a hierarchical Bayesian principle, the method takes both systematic and statistical measurement errors into account, which has not…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in…
In this article, we derive a theoretical formalism that unifies the rigorous coupled wave analysis and the dynamical diffraction theory. Based on this formalism, we design a computational approach for the diffraction calculation for the…